Model-based optimization of GKP quantum error correction with Feedback-GRAPE

Bosonic codes offer the advantageous possibility of storing the logical information of a qubit in a single component device, exploiting the infinitely large Hilbert space of an harmonic oscillator. In particular, the Gottesman-Kitaev-Preskill (GKP) code has recently been demonstrated to be correctable far beyond the break-even point of the best passive encoding in the same system [1]. In our work, we have demonstrated that it is possible to exploit a model-based deep-learning approach (so-called Feedback-GRAPE [2]) to optimize the parameters of a quantum error correction circuit for the GKP code [3]. In particular, we investigate the use of non-Markovian strategies, represented by a recurrent neural network.

[1] V.V.Sivak et al., Real-time quantum error correction beyond break-even, Nature 616, 50-55 (2023)

[2] R. Porotti et al., Gradient-Ascent Pulse Engineering with Feedback, PRX Quantum 4, 030305

[3] M. Puviani et al., Model-based optimization of GKP quantum error correction with real-time feedback, in preparation